Solve for $x$ and $y$ using elimination. ${4x+6y = 76}$ ${3x+2y = 42}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-3$ ${4x+6y = 76}$ $-9x-6y = -126$ Add the top and bottom equations together. $-5x = -50$ $\dfrac{-5x}{{-5}} = \dfrac{-50}{{-5}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {4x+6y = 76}\thinspace$ to find $y$ ${4}{(10)}{ + 6y = 76}$ $40+6y = 76$ $40{-40} + 6y = 76{-40}$ $6y = 36$ $\dfrac{6y}{{6}} = \dfrac{36}{{6}}$ ${y = 6}$ You can also plug ${x = 10}$ into $\thinspace {3x+2y = 42}\thinspace$ and get the same answer for $y$ : ${3}{(10)}{ + 2y = 42}$ ${y = 6}$